Kim Yoosun Jamie, Cribbie Robert A
Quantitative Methods Program, Department of Psychology, York University, Toronto, Ontario, Canada.
Br J Math Stat Psychol. 2018 Feb;71(1):1-12. doi: 10.1111/bmsp.12103. Epub 2017 Jun 1.
Valid use of the traditional independent samples ANOVA procedure requires that the population variances are equal. Previous research has investigated whether variance homogeneity tests, such as Levene's test, are satisfactory as gatekeepers for identifying when to use or not to use the ANOVA procedure. This research focuses on a novel homogeneity of variance test that incorporates an equivalence testing approach. Instead of testing the null hypothesis that the variances are equal against an alternative hypothesis that the variances are not equal, the equivalence-based test evaluates the null hypothesis that the difference in the variances falls outside or on the border of a predetermined interval against an alternative hypothesis that the difference in the variances falls within the predetermined interval. Thus, with the equivalence-based procedure, the alternative hypothesis is aligned with the research hypothesis (variance equality). A simulation study demonstrated that the equivalence-based test of population variance homogeneity is a better gatekeeper for the ANOVA than traditional homogeneity of variance tests.
传统独立样本方差分析程序的有效使用要求总体方差相等。先前的研究调查了诸如Levene检验等方差齐性检验作为确定何时使用或不使用方差分析程序的把关方法是否令人满意。本研究聚焦于一种采用等效性检验方法的新型方差齐性检验。基于等效性的检验不是针对方差不相等的备择假设来检验方差相等的原假设，而是针对方差差异落在预定区间之外或边界上的原假设，检验方差差异落在预定区间内的备择假设。因此，对于基于等效性的程序，备择假设与研究假设（方差相等）一致。一项模拟研究表明，基于等效性的总体方差齐性检验比方差齐性的传统检验更适合作为方差分析的把关方法。
